# Phase 3: OECD Null Resolution — Competing Hypotheses


## ca_gdp

| Model | Z₁ | Z₁×OECD | Z₁×High | Z₁×KAopen | N | R² |
|---|---|---|---|---|---|---|
| M1_baseline | 29.765** | -- | -- | -- | 7624 | 0.025 |
| M2_oecd | 22.457 | -52.375 | -- | -- | 7624 | 0.033 |
| M3_income_oecd | 8.745 | -103.075* | 82.955** | -- | 7624 | 0.055 |
| M4_kaopen_oecd | 25.119** | -45.317 | -- | 5.325 | 6780 | 0.061 |
| M5_horserace | 3.547 | -108.340** | 107.493*** | -5.750 | 6780 | 0.087 |

## gross_savings_gdp

| Model | Z₁ | Z₁×OECD | Z₁×High | Z₁×KAopen | N | R² |
|---|---|---|---|---|---|---|
| M1_baseline | 114.147*** | -- | -- | -- | 6642 | 0.130 |
| M2_oecd | 127.168*** | -119.086* | -- | -- | 6642 | 0.131 |
| M3_income_oecd | 134.205*** | -99.338 | -28.019 | -- | 6642 | 0.184 |
| M4_kaopen_oecd | 120.995*** | -97.942 | -- | -9.046 | 5885 | 0.126 |
| M5_horserace | 111.661*** | -106.628 | 22.500 | -12.323 | 5885 | 0.181 |

## gross_investment_gdp

| Model | Z₁ | Z₁×OECD | Z₁×High | Z₁×KAopen | N | R² |
|---|---|---|---|---|---|---|
| M1_baseline | 32.616*** | -- | -- | -- | 6620 | 0.068 |
| M2_oecd | 36.412*** | -7.893 | -- | -- | 6620 | 0.069 |
| M3_income_oecd | 39.857*** | 1.381 | -16.014 | -- | 6620 | 0.072 |
| M4_kaopen_oecd | 35.994*** | -16.837 | -- | -1.842 | 5857 | 0.088 |
| M5_horserace | 32.955** | -19.454 | 5.077 | -2.403 | 5857 | 0.090 |

## Interpretation

- **H1 (Income)**: If Z₁×OECD loses significance when Z₁×High is added, OECD proxies for income.
- **H2 (Openness)**: If Z₁×OECD loses significance when Z₁×KAopen is added, OECD proxies for financial openness.
- **H3 (Institutional)**: If Z₁×OECD survives all controls, OECD membership itself attenuates demographic effects.

*PanelGLS with AR(1) correction. \*p<0.1, \*\*p<0.05, \*\*\*p<0.01*
